/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

Problem:
 +(1(),x) -> +(+(0(),1()),x)
 +(0(),x) -> x

Proof:
 Extended Uncurrying Processor:
  application symbol: +
  symbol table:
   0 ==> 00/0 01/1 02/2
   1 ==> 10/0 11/1
   
  uncurry-rules:
   +(10(),x2) -> 11(x2)
   +(01(x4),x5) -> 02(x4,x5)
   +(00(),x4) -> 01(x4)
  eta-rules:
   +(+(0(),x),x1) -> +(x,x1)
  problem:
   11(x) -> 02(10(),x)
   01(x) -> x
   02(x,x1) -> +(x,x1)
   +(10(),x2) -> 11(x2)
   +(01(x4),x5) -> 02(x4,x5)
   +(00(),x4) -> 01(x4)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                   [1 0 1]       
    [02](x0, x1) = [0 1 0]x0 + x1
                   [1 0 0]       ,
    
                    [0]
    [01](x0) = x0 + [1]
                    [1],
    
           [1]
    [00] = [1]
           [0],
    
                    [0]
    [11](x0) = x0 + [1]
                    [0],
    
           [0]
    [10] = [1]
           [0],
    
                  [1 0 1]       
    [+](x0, x1) = [0 1 0]x0 + x1
                  [1 0 0]       
   orientation:
                [0]        [0]             
    11(x) = x + [1] >= x + [1] = 02(10(),x)
                [0]        [0]             
    
                [0]         
    01(x) = x + [1] >= x = x
                [1]         
    
               [1 0 1]          [1 0 1]                
    02(x,x1) = [0 1 0]x + x1 >= [0 1 0]x + x1 = +(x,x1)
               [1 0 0]          [1 0 0]                
    
                      [0]         [0]         
    +(10(),x2) = x2 + [1] >= x2 + [1] = 11(x2)
                      [0]         [0]         
    
                   [1 0 1]          [1]    [1 0 1]                   
    +(01(x4),x5) = [0 1 0]x4 + x5 + [1] >= [0 1 0]x4 + x5 = 02(x4,x5)
                   [1 0 0]          [0]    [1 0 0]                   
    
                      [1]         [0]         
    +(00(),x4) = x4 + [1] >= x4 + [1] = 01(x4)
                      [1]         [1]         
   problem:
    11(x) -> 02(10(),x)
    01(x) -> x
    02(x,x1) -> +(x,x1)
    +(10(),x2) -> 11(x2)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                    [1 0 1]     [1 0 0]  
     [02](x0, x1) = [1 1 0]x0 + [0 0 0]x1
                    [0 0 1]     [0 0 0]  ,
     
                     [1]
     [01](x0) = x0 + [0]
                     [0],
     
                [1 0 0]     [0]
     [11](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0],
     
            [0]
     [10] = [1]
            [0],
     
                   [1 0 0]     [1 0 0]  
     [+](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  
    orientation:
             [1 0 0]    [0]    [1 0 0]    [0]             
     11(x) = [0 0 0]x + [1] >= [0 0 0]x + [1] = 02(10(),x)
             [0 0 0]    [0]    [0 0 0]    [0]             
     
                 [1]         
     01(x) = x + [0] >= x = x
                 [0]         
     
                [1 0 1]    [1 0 0]      [1 0 0]    [1 0 0]            
     02(x,x1) = [1 1 0]x + [0 0 0]x1 >= [0 1 0]x + [0 0 0]x1 = +(x,x1)
                [0 0 1]    [0 0 0]      [0 0 0]    [0 0 0]            
     
                  [1 0 0]     [0]    [1 0 0]     [0]         
     +(10(),x2) = [0 0 0]x2 + [1] >= [0 0 0]x2 + [1] = 11(x2)
                  [0 0 0]     [0]    [0 0 0]     [0]         
    problem:
     11(x) -> 02(10(),x)
     02(x,x1) -> +(x,x1)
     +(10(),x2) -> 11(x2)
    Unfolding Processor:
     loop length: 3
     terms:
      11(x39)
      02(10(),x39)
      +(10(),x39)
     context: []
     substitution:
      x39 -> x39
     Qed